Related papers: Balancedly splittable orthogonal designs and equia…
A geometric approach to understanding recursion relations for scattering amplitudes is developed. We achieve this by studying intersection numbers of triangulated accordiohedra presented as hyperplane arrangements. The cancellation of…
Equiangular tight frames are examples of Grassmannian line packings for a Hilbert space. More specifically, according to a bound by Welch, they are minimizers for the maximal magnitude occurring among the inner products of all pairs of…
This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…
An approach is proposed which, given a family of linearly independent functions, constructs the appropriate biorthogonal set so as to represent the orthogonal projector operator onto the corresponding subspace. The procedure evolves…
We introduce a new system of split variational inequality problems which is a natural extension of split variational inequality problem in semi-inner product spaces. We use the retraction technique to propose an iterative algorithm for…
We give explicit constructions for incomplete pairwise balanced designs IPBD$((v;w),K)$, or, equivalently, edge-decompositions of a difference of two cliques $K_v \setminus K_w$ into cliques whose sizes belong to the set $K$. Our…
A hypercomplex structure on a differentiable manifold consists of three integrable almost complex structures that satisfy quaternionic relations. If, in addition, there exists a metric on the manifold which is Hermitian with respect to the…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
The aim of the paper is to present the integrable systems on partial isometries which are related to the restricted Grassmannian in finite dimensional context. Some explicit solutions are obtained.
New splitting theorems in a semi-Riemannian manifold which admits an irrotational vector field (not necessarily a gradient) with some suitable properties are obtained. According to the extras hypothesis assumed on the vector field, we can…
In this paper we define "piecewise scalable frames". This new scaling process allows us to alter many frames to Parseval frames which is impossible by the previous standard scaling. We give necessary and sufficient conditions for a frame to…
A triangulation of a polygon has an associated Stanley-Reisner ideal. We obtain a full algebraic and combinatorial understanding of these ideals, and describe their separated models. More generally we do this for stacked simplicial…
We study bounded remainder sets with respect to an irrational rotation of the $d$-dimensional torus. The subject goes back to Hecke, Ostrowski and Kesten who characterized the intervals with bounded remainder in dimension one. First we…
Using the orthogonal connectedness, we introduce the notion of orthogonal decomposability of convex polytopes and study it in the case of Platonic and Archimedean solids. While doing so, we also encounter polytopes which are not…
Recently, the eigenvalue problems formulated with symmetric positive definite bilinear forms have been well investigated with the aim of explicit bounds for the eigenvalues. In this paper, the existing theorems for bounding eigenvalues are…
Rectangular designs are classified as regular, Latin regular, semiregular, Latin semiregular and singular designs. Some series of selfdual as well as alpharesolvable designs are obtained using matrix approaches which belong to the above…
Recent advances in cutting-plane strategies applied to robust optimization problems show that they are competitive with respect to problem reformulations and interior-point algorithms. However, although its application with polyhedral…
In this work, we explore the use of operator splitting algorithms for solving regularized structural topology optimization problems. The context is the classical structural design problems (e.g., compliance minimization and compliant…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
We offer some partition functions related to ternary quadratic forms, and note on their upper bounds and related properties. We offer these results as an application of a simple method related to conjugate Bailey pairs presented in a prior…